| This thesis gives a more systematical study to the correlative problems in the melting law of metal at high pressure, such as equation of state, melting criterion, the material strength in melting region, melting mechanism and the analyse and process of experimental data:(1) The effective Grüneisen coefficient proposed by Anderson has been applied in geophysics and in the calculation of the iron's meling curve and the results shows that it is a good method. According to the effective Grüneisen coefficient conception and basing on the three term equation of state, we derived the effective Grüneisen equation of state. As an evolution, a new method to calculate shock temperature was proposed, the calculated results with some metals agree with experimental data well.(2) Proposing a melting criterion constraint with 0K equation of state. This melting criterion can picture the high pressure melting curve of metal. Its physical mechanism was givn in the thesis by theoretical analysis and comparing molecular dynamics simulation. It has the same physical meaning as Lindemann melting criterion and the melting criterion given by mean field approach in some conditions.(3) All the proposed high pressure and high temperature constitutive equations have a same limitation, i.e. they can not give the correct behavior of shear modulus in the solid-liquid mixing phase. By introducing the internal energy as power weight, we built a constitutive equation up to liquidus and which has no such a limition. With it, the shear modulus of aluminum along Hugoniot path was calculated, the results agreed experimental data and showed that the chang of shear modulus can be divided into three stages, that is, work hardening, temperature softening and melting.(4) Discussing and analyzing the behavior of shear modulus in solid liquid mixing phase region with Percolation and Renormalized Group. The propagating process of sound in the melting material was analysed with Huygens principle. Then the critical melting mass function was calculated by using percolation and the results were that, at the critical melting mass function 0.313, a percolating liquid region appeared in the melting material, which was just corresponding to the turning point of longitudinal to bulk sound velocity; when melting mass fuction was larger than 0.687, there would be no percolation solid region in the material and this meaned that the shear modulus equaled zero. The analyzing results with percolation also indicated that the method, which was used to determine the shock induced melting region with sound velocities in shock compression experiment, had errors. By analyzing the constitution of liquid and solid of material in melting region along shearing plane, the behavior of shear modulus in melting region is predicted by renormalization group theory and is coincidence with that given by percolation theory.(5) Taking the completing point of shock induced melting region as referring point, the problem, which has been puzzling for a long time, was solved by Huang Haijun. But at the initial point of shock induced melting region, how to modify the shock temperature to the equilibrium melting temperature still is not solved. Using the calculated critical melting mass function and basing the superheating model proposed by Luo et al, we amend the shock temperatue of iron at the initial point of shock induced melting region. The amended equilibrium melting temperature, together with the calculated result by Huang Haijun, the Ma's and Shen's static experimental data, is on the same Lindemann melting curve.(6) With the SC experimental means and optical analyzing method, we measured the interfacial temperatures of Ly12Al/LiF around the pressure 100GPa. These interfacial temperature can thought as melting temperature by considering the gap effection.
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